WASHINGTON - Mitt Romney unveiled a sweeping budget-cutting plan yesterday that would make significant cuts to Social Security, Medicare, and Medicaid and dramatically shrink the federal government, slashing funding to Amtrak and programs supporting the arts and public broadcasting.

If elected president, the former Massachusetts governor said, he would gradually increase the eligibility age for Medicare and Social Security and turn Medicaid into a block-grant program that would cap payments to states for health care for the poor and disabled at fixed amounts.

Amtrak would lose all government subsidies, and Romney would slice $600 million from the National Endowment for the Arts and Humanities, the Corporation for Public Broadcasting, and the Legal Services Corporation, which subsidizes legal services for the poor.

“There are some who are going to argue that fiscal responsibility is heartless and immoral,’’ Romney said. “No, what’s heartless is to imperil our children, and what’s immoral is to imperil the strength of a nation that was founded under God and preserved by his hand.’’

Another $300 million would be cut from subsidies for family planning and tests for sexually transmitted diseases and cervical cancer, on the grounds that the funds indirectly support groups that provide “abortions or abortion-related services.’’

Overall, the plan would cut some $500 billion annually from the federal budget as of 2016, he said in a speech at the Defending the American Dream summit of Americans for Prosperity.

Romney campaign advisers said the pace and scope of changes to Social Security, Medicare, and Medicaid had yet to be decided, but they said current and soon-to-be beneficiaries would not be affected.

The plan resembles one released earlier this year by Representative Paul Ryan, the Republican chairman of the House Budget Committee, who also proposed capping Medicaid payments to states and converting them into block grants. But Ryan’s plan would have privatized Medicare, the federal health care insurance for seniors. Romney’s plan would allow seniors to choose between private insurance and Medicare.

Romney said his plan will lead to a “simpler, smaller, and smarter’’ federal government.

Since officially hitting the campaign trail in the spring, Romney has issued a number of detailed policy statements, including a 160-page jobs plan. He is running largely on his business acumen at a time when the US economy is stagnating and the national debt is climbing to its highest level, more than $14 trillion.

Aides to other candidates for the Republican presidential nomination were quick to slam Romney’s plan yesterday. A spokesman for former Utah governor Jon Huntsman said that the proposal does not go far enough, that it only “nibbles around the edges on entitlements,’’ and that Ryan’s plan is better.

Romney “pandered to interest groups and offered timid reforms to government spending, all the while trying to convince voters that he will magically balance the budget anyway,’’ spokesman Tim Miller said.

Representative Ron Paul’s campaign also said Romney’s plan does not cut enough, saying defense spending also should face the ax.

“Dr. Paul remains the only candidate with a plan to cut spending deep enough to balance the budget right away as Governor Romney’s proposal leaves steep deficits for years to come and is unlikely to save us from the debt crisis looming on the horizon,’’ said Paul’s campaign chairman, Jesse Benton.

A spokesman for President Obama’s reelection campaign, Ben LaBolt, said Romney’s proposed cuts would place an untenable burden on middle-class and elderly Americans. LaBolt equated Romney’s plans for overhauling Medicare with privatization.

“The fundamental challenge of our time is how we rebuild our economy so that hard work and responsibility are rewarded and that economic security is restored for the middle class,’’ LaBolt said in a statement. “Mitt Romney’s proposal takes us in exactly the opposite direction.’’

On his first day in office, Romney said, he would send Congress a bill cutting all non-defense spending by 5 percent. Also on his first day, he said, he would begin work to repeal Obama’s overhaul of health insurance, which Romney said would save the government $95 billion.

Eliminating Amtrak subsidies would save $1.6 billion annually, the campaign estimated. It said capping Medicaid payments to states and funding for other programs, such as workforce training, would save $100 billion.

Romney characterized the changes to entitlement programs as preservation measures. Providing Medicare benefits to an increasing number of older Americans who are living longer than ever before is unsustainable, he said.

Under Romney’s plan, some Medicare benefits would be provided on a sliding scale, based on income. Currently, the same benefits are provided to every senior. The eligibility age would increase gradually and be tied to increases in life expectancy.

“These ideas will give tomorrow’s seniors the same kinds of choices that most Americans have in their health care today,’’ Romney said. “The future of Medicare should be marked by competition, choice, and innovation - rather than bureaucracy, stagnation, and bankruptcy.’’

“The thing that I really like is a presidential candidate who is willing to show some specifics,’’ said Haskins, who served as a welfare policy adviser to President George W. Bush. “That’s really good.’’

In particular, Haskins praised Romney for proposing deep cuts in spending to try to control the federal deficit. “The things he proposes are tough, but they’ve got to be,’’ he said. Haskins said, however, it was unrealistic of Romney to require the federal government to spend no more than 20 percent of the gross national product, as his plan provides, given the rapid growth of Medicare and Social Security.

Haskins was also critical of Romney for refusing to include any tax increases in his plan. Haskins said that position will make it impossible to balance the budget and strike a deal with Democrats in Congress.

“You’ve got to have revenues, and it’s time for Republicans to admit that,’’ said Haskins, a Republican. “You’ve got to have a compromise.’’

Michael Levenson of the Globe staff contributed to this report. Donovan Slack can be reached at dslack@globe.com. Follow her on Twitter @DonovanSlack.

BostonGlobe.com complimentary digital access has been provided to you, without a subscription, for free starting today and ending in 14 days. After the free trial period, your free BostonGlobe.com digital access will stop immediately unless you sign up for BostonGlobe.com digital subscription. Current print and digital subscribers are not eligible for the free trial.

Thanks & Welcome to Globe.com

You now have unlimited access for the next two weeks.

BostonGlobe.com complimentary digital access has been provided to you, without a subscription, for free starting today and ending in 14 days. After the free trial period, your free BostonGlobe.com digital access will stop immediately unless you sign up for BostonGlobe.com digital subscription. Current print and digital subscribers are not eligible for the free trial.